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Chapter 2: Q. 104 (page 71)

Profit Function Suppose that the revenue R, in dollars, from selling x clocks is R(x)=30x. The cost C, in dollars, of selling x clocks is C(x)=0.1x2+7x+400.

(a) Find the profit function, P(x)=R(x)-C(x).

(b) Find the profit if x=30clocks are sold.

(c) Interpret P(30).

Short Answer

Expert verified

(a) The profit function is P(x)=-0.1x2+23x-400

(b) The profit is $200if hundred cell phones are sold.

(c) When 30 clocks are sold, the profit is $200.

Step by step solution

01

Step 1. Given Information

Profit Function Suppose that the revenue R, in dollars, from selling xclocks is R(x)=30x. The cost C, in dollars, of selling xclocks is role="math" localid="1646411590420" C(x)=0.1x2+7x+400.

(a) Find the profit function, P(x)=R(x)-C(x).

(b) Find the profit if x=30clocks are sold.

(c) Interpret P(30).

02

Part (a) Step 1. We have to find the profit function P(x)=R(x)-C(x)

The value of R(x)=30xandC(x)=0.1x2+7x+400

03

Part (a) Step 2. Putting the value in the equation of profit. 

P(x)=30x-(0.1x2+7x+400)P(x)=30x-0.1x2-7x-400

Simplify

role="math" localid="1646411303541" P(x)=-0.1x2+23x-400

04

Part (b) Step 1. We have to find the profit if x=30 clocks phones are sold.Putting x=30 in the function of profit.

P(30)=-0.1(30)2+23脳30-400P(30)=-0.1脳900+23脳30-400P(30)=-90+690-400P(30)=200

05

Part (c) Step 1. We have to interpret P(30)

When 30 clocks are sold, the profit is $200.

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